# IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 105 - 112 of 968

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## Question number: 105

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MCQ▾

### Question

If are two numbers such that . Then are the roots of the quadratic equation ________

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 106

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MCQ▾

### Question

The difference of roots of the quadratic equation is ________

### Choices

Choice (4)Response

a.

-9

b.

-10

c.

10

d.

9

## Question number: 107

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MCQ▾

### Question

Degree of polynomial is ________

### Choices

Choice (4)Response

a.

6

b.

1

c.

3

d.

4

## Question number: 108

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MCQ▾

### Question

The value of k for which the system of equations has a non-zero solution, is ________

### Choices

Choice (4)Response

a.

0

b.

8

c.

6

d.

2

## Question number: 109

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MCQ▾

### Question

When is divided by , the quotient and remainder is ________

### Choices

Choice (4)Response

a.

, -4

b.

c.

, 4

d.

## Question number: 110

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MCQ▾

### Question

The value of k for which the system of equations , has infinite number of solutions, is ________

### Choices

Choice (4)Response

a.

3

b.

1

c.

6

d.

0

## Question number: 111

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MCQ▾

### Question

If one zero of the polynomial is a reciprocal of the other, then p is equal to ________

### Choices

Choice (4)Response

a.

4

b.

6

c.

8

d.

7

## Question number: 112

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MCQ▾

### Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. If x represents the speed of the boat in still water in km/hr and y represent the speed of the stream in km/hr, then ________

### Choices

Choice (4)Response

a.

b.

c.

d.

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